# Dipole vector associated with charges

## Homework Statement

Problem attached in Dipole.Jpg

## The Attempt at a Solution

I am fine with Part A of the problem. Im just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!

#### Attachments

• Dipole.jpg
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I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.

Orodruin
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They are asking for the dipole moment associated with the two charges. The dipole moment relative to a point is given by summing the charge multiplied by the position vector over all charges. For an overall neutral charge configuration, this does not depend on the point. The dipole moment is not the electric field.

I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.
You cannot solve B without using an expression for the dipole moment since the problem asks you to find the dipole moment. This part of the problem has nothing to do with the part of finding the field at p.

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I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.

Orodruin
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Im just trying to understand what part B is asking.

The issue is understanding that the dipole moment is not the electric field, but what I described in #3.

SammyS
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## Homework Statement

Problem attached in Dipole.Jpg

## The Attempt at a Solution

I am fine with Part A of the problem. Im just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.

#### Attachments

• dipole-jpg.jpg
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Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? Ive attached my logic "dipole problem.JPG"

#### Attachments

• Dipole problem.JPG
32.7 KB · Views: 186
I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.
Yes I believe I was mixing equations up from the book, my notes, and my head. I will look at D now and see if I can make sense of that one. Thanks!

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A detailed analysis of the dipole formulas show that they are intended for distances ## r>>d ## and will not work at close range. In this sense, in this combination of 4 questions, (b) and (c) are really unrelated and are misleading you. The results in (b) and (c) can not be used to solve part (d).

View attachment 230535

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.
Ahh, okay. I guess thats true. So
Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? Ive attached my logic "dipole problem.JPG"
Okay, Just read some responses. So this is not correct then. Ill go back and read on what Dipole Vector means.

SammyS
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For the OP: All they are asking for in parts (b) and (c) is at the top part of this "link": http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dipole.html
Thanks for the link. Is it true that the statement " what is the magnitude and and direction of the dipole vector" is referring to the dipole moment? and If so it would be
P=Qa(-i) ?

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To give you a quick introduction to it, the ## \frac{1}{r^3} ## behavior of electric and magnetic dipoles is actually very useful in analyzing some rather advanced E&M (electricity and magnetism) problems, and is used in the computation of the electric and/or magnetic fields at a distance from what are microscopic dipoles (with very small ## d ##). ## \\ ## In this problem, they are teaching you in parts (b) and (c) a couple of simple definitions, but nothing more than that. The ## \frac{1}{r^3} ## formulas do not apply at very close range=they do not give a correct result.

SammyS
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Thanks for the link. Is it true that the statement " what is the magnitude and and direction of the dipole vector" is referring to the dipole moment? and If so it would be
P=Qa(-i) ?
For part (b): Yes .

For part (b): Yes .
Okay, therefore part C would be:
P=2Qa(i)

SammyS
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Okay, therefore part C would be:
P=2Qa(i)
Yes.